Jeremy Corbyn is inching closer to backing a second referendum, with the Labour leader under intense pressure from senior figures including Keir Starmer to prevent more restive MPs from leaving the party and spike the guns of the splitters.

At a Brexit policy meeting this week, Starmer spoke out in favour of an amendment drawn up by the Labour MPs Peter Kyle and Phil Wilson, the Guardian understands. Under the terms of the amendment, MPs would support the prime minister’s deal in exchange for it being put to a public vote.

Other supporters of a second referendum, including the shadow home secretary, Diane Abbott, have expressed more scepticism about the approach envisaged by the amendment.

The idea of supporting a more straightforward, pro-referendum amendment also remains in play, the Guardian understands. “If there was a freestanding second referendum amendment on its own we would have to vote for it,” said one shadow minister.

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The eight former Labour MPs who split from the party this week to form the Independent Group in the Commons all back a second referendum, and have attacked Corbyn for what they perceive as a “betrayal” on Brexit.

Starmer and the shadow chancellor, John McDonnell, were charged with meeting Kyle and Wilson to discuss the precise wording of the amendment, which would not be tabled until May brings her final deal back to parliament for the “meaningful vote”.

If that does not happen next week, May has promised to table another amendable motion, like the one that resulted in her being defeated by Brexit rebels this month.

Labour is likely to table its own amendment to that motion, which would put forward Corbyn’s alternative Brexit policy. It will also back efforts spearheaded by the Labour MP Yvette Cooper to secure an extension to article 50 if a deal is not ratified in time for exit day.

Speaking in Brussels on Thursday, Corbyn sounded markedly warmer towards the idea of a second referendum than in recent weeks. Following meetings with senior EU officials, the Labour leader called for the prime minister to back a customs union in order to build a Commons majority for the Brexit deal.

He told reporters his discussions confirmed that Labour’s proposals, which include having a say in the bloc’s trade policy, were “credible”. But Corbyn said the option of holding a second referendum, should May fail to back a close economic partnership with the EU, remained “very much part of the agenda put forward by the Labour party”.

Some key figures, including Corbyn’s close ally Jon Trickett and the party chair, Ian Lavery, remain deeply sceptical about the merits of a public vote on the Brexit deal, fearing the impact on Labour’s popularity in Brexit constituencies.

Peter Kyle has said his amendment, which could lead to a second referendum, is ‘100% in play’. Photograph: PjrNews/Alamy Stock Photo/Alamy Stock Photo

But Starmer and Labour’s deputy leader, Tom Watson, are keen to avoid the party providing a pretext for any further departures.

Abbott is understood to have argued that as a longtime supporter of enhancing party democracy, it was hard for Corbyn to ignore the voice of Labour members, who are overwhelmingly pro-remain. Up to 10 shadow ministers have said they would be prepared to resign rather than vote against a second referendum amendment.

Some senior party figures believe much of the appeal of the 11-strong Independent Group would be neutralised if Labour leant towards backing a referendum.

Kyle said his amendment was “100% in play” and he was hopeful that Labour’s leadership would back it. To allay concerns it would require Labour to back May’s deal, he said the party could abstain, allowing the deal to pass the Commons with Conservative votes.

“I recognise that is a compromise, and compromises are not meant to be totally comfortable. But it would end the Brexit nightmare by ensuring there was a confirmatory vote after Theresa May’s deal passed through parliament,” he said.

Kyle said, if Corbyn and Labour’s leadership do not vote for his amendment, “I believe that the divisions in our party would rapidly grow”. Asked if he would consider defecting if Labour was not prepared to support a second referendum, he said: “I will not be making any threats over this.”

Labour members continue to press for a second referendum in local constituencies. On Thursday night, members of the Islington South constituency party voted in support of a second referendum with the local MP, the shadow foreign secretary, Emily Thornberry, in attendance.

Thornberry had urged members not to pass the motion, and hinted there would be developments in Labour’s position in the coming days.

At last month’s Brexit vote, Corbyn proposed a Commons vote on the options, including his alternative Brexit plan, and whether to legislate “to hold a public vote on a deal”.

Speaking in Brussels, he said the option of a second referendum would remain key to Labour’s strategy for next Wednesday, when the Commons is due to vote again on the Brexit options.

“We will put a motion to parliament, as I have already,” Corbyn said. “Keir Starmer and I have put a motion to parliament, which included the option of a popular vote to confirm otherwise agreements that have been reached. That was rejected by parliament at that stage. Clearly it is very much part of the agenda put forward by the Labour party.”

Corbyn, who met the European commission secretary-general, Martin Selmayr, during his day in Brussels, made his comments shortly after the commission president said he was not optimistic about the chances of avoiding a no-deal Brexit.

EU diplomats briefed on recent meetings involving the prime minister and the Labour leader with Brussels officials said the risk of a no-deal Brexit had increased in recent days.

May told the European commission president, Jean-Claude Juncker, on Monday that she would not seek to extend article 50 despite the lack of progress towards a deal. Corbyn told Selmayr and Michel Barnier, the main EU negotiator, that he was determined to avoid a no-deal Brexit.

But ambassadors were advised that Corbyn appeared more concerned with triggering a general election if he could.

Juncker, who held talks with May on Wednesday night, said: “If no deal were to happen, and I cannot exclude this, this would have terrible economic and social consequences in Britain and on the continent, so my efforts are oriented in a way that the worst can be avoided. But I am not very optimistic when it comes to this issue. Because in the British parliament every time they are voting, there is a majority against something; there is no majority in favour of something.”

Stephen Barclay, the Brexit secretary, and the attorney general, Geoffrey Cox, were to meet the EU’s chief negotiator, Michel Barnier, later on Thursday.

Corbyn said he feared the prime minister was “running down the clock” in the negotiations. “We put forward what we believe to be a credible process which would be to negotiate a customs union with the EU and alignment to ensure market access,” he said.

“We are strongly of the belief that these proposals are credible. That has been confirmed by our meetings today. The problem is the prime minister is insisting on her deal, which has already been defeated very heavily in parliament, and running down the clock by trying to keep the threat of no deal on the table with all the damage that does.”